The divergence of a vector function A is a scalar function defined by (a) Verify that div [grad g(x, y, z)] ¡ g = 2g/x2

The divergence of a vector function A is a scalar function defined by

(a) Verify that div [grad g(x, y, z)] ‰¡ ˆ‡ ˆ™ ˆ‡g = ˆ‚2g/ˆ‚x2 + ˆ‚2g/ˆ‚y2 + ˆ‚2g/ˆ‚z2. This is the origin of the notation ˆ‡2 for 02/ˆ‚x2 + ˆ‚2/ˆ‚y2 + ˆ‚2/ˆ‚z2.
(b) Find ˆ‡ ˆ™ r, where r = ix + jy + kz.